Ratio, Proportion & Partnership: Ration, Rule, Proportion, Rate, Partnership

Ratio: A ratio is a comparison of two quantities in the same units. We generally separate the two quantities in the ratio with a colon (:). Suppose, we want to write the ratio of 8 and 12. We can write this as 8 : 12 or as a faction 8/12
First term of a ratio is called antecedent, while the second term is known as consequent. Here, 8 is antecedent & 12 is consequent.

Rule: Multiplication or division of each term of a ratio by a same non-zero number does not affect the ratio.
Ratio of 8 & 12 = 8:12 = 8/12 = 4/6 = 2/3 = 10/15 = 14/21
i.e 8:12 = 4:6 = 2:3 = 10:15 = 14:21
3:4 = 2x3:4x2 = 6:8
10:5 = 10/5:5/5 = 12:1

Proportion: A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal. Simply, the equality of two ratios is called proportion.
3/4 =6/8 or 3:4 = 6:8 is an example of proportion.
From 2/3 = 6/9
We can write, 2x9 = 3x6 [Cross-multiplication]

Rate: A rate is a ratio that expresses how long it takes to do something, such as traveling a certain distance. To walk 3 kilometers in one hour is to walk at the rate of 3 km/hr. The fraction expressing a rate has units of distance in the numerator and units of time in the denominator.

Ratio is a relationship: a number of people to a number of people; an amount of money to an amount of money.
<> A:B = 2:3; B:C = 3:4
:. A:B:C = 2:3:4
<> A:B = 2:3; B:C = 4:5
A:B = 2:3 = 2x4:3x4 = 8:12
B:C = 4:5 = 4x3: 5x3 = 12:15
:. A:B:C = 8:12:15

Partnership: Whenever two or more people involve in a business, invest their money and share profit according to the ratio of the ratio of their investment, partnership arises.

For example:
* A, B & C form a partnership & invest $60,000 $80,000 & $100,000 respectively. After one year, they receive $24,000 as profit. What will be the profit of each?

Explore: Ratio of investment
= 60,000 : 80,000 : 100,000
= 60 : 80 : 100
= 6 : 8 : 10
= 3 : 4 : 5
Sum of the numbers = 3+4+5 = 12
:. Profit of A = $24,000 x (3/12) = $6,000
Profit of A = $24,000 x (4/12) = $8,000
Profit of A = $24,000 x (5/12) = $10,000

*Divide 70 chocolates among girls & boys, where ratio of girls to boys is 3:4.

Explore: Ratio of girls to boys = 3:4
Sum of the terms = 3+4 = 7
:. Girls will get = 70 x (3/7) = 30 Chocolates
Boys will get = 70 x (4/70) =40 Chocolates

* 3:X = 2:6, X = ?

Explore: 3:X = 2:6
=> 3/X = 2/6
=> 3x6 = 2xX
=> X = 18/2 = 9
Answer: X = 9

Posted in: Partnership, Proportion, Ratio